QCE Physics - Unit 4 - Quantum theory
Bohr Model and Line Spectra | QCE Physics
Learn QCE Physics Bohr model, hydrogen line spectra, quantised angular momentum, standing waves and Rydberg calculations.
Updated 2026-06-15 - 4 min read
QCAA official coverage - Physics 2025 v1.3
Exact syllabus points covered
- Compare the different models of the atom proposed by Rutherford and Bohr.
- Explain how Bohr's model of the hydrogen atom integrates light quanta and atomic energy states to explain the specific wavelengths in the hydrogen line spectrum.
- Solve problems involving the line spectra of simple atoms using atomic energy states or atomic energy level diagrams using $n\lambda = 2\pi r$, $mvr = \frac{nh}{2\pi}$, $\frac{1}{\lambda} = R\left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)$ and $\lambda = \frac{h}{p}$.
- Describe wave-particle duality of light by identifying evidence that supports the wave characteristics of light and evidence that supports the particle characteristics of light.
Line spectra show that atoms do not emit or absorb every possible wavelength. They emit and absorb specific wavelengths, which means atomic energy changes are quantised. Bohr's model explained this for hydrogen by combining atomic structure with light quanta.
Original Sylligence diagram for physics bohr line spectra map.
Rutherford compared with Bohr
Rutherford's nuclear model placed a small positive nucleus at the centre of the atom, with electrons outside it. This explained scattering evidence, but it had a serious problem: classical physics predicted orbiting electrons should radiate energy continuously and spiral into the nucleus.
Bohr's model kept the nucleus but added quantised electron orbits. Electrons could occupy only certain allowed energy levels. They did not radiate energy while staying in one allowed level. Radiation was emitted or absorbed only when an electron moved between levels.
This made the hydrogen line spectrum explainable. Instead of a continuous rainbow, hydrogen produces discrete lines because only certain energy transitions are allowed.
Quantised angular momentum and standing waves
Bohr proposed that angular momentum is quantised:
$ mvr=\frac{nh}{2\pi} $
where $n$ is a positive integer. This condition links the electron's motion to allowed orbit sizes.
The standing-wave version is:
$ n\lambda=2\pi r $
This says a whole number of de Broglie wavelengths must fit around the orbit. If the wave does not fit neatly, it interferes with itself and is not an allowed stable state.
Energy level transitions
When an electron drops from a higher energy level to a lower energy level, a photon is emitted. When an electron absorbs a photon with exactly the right energy, it can jump to a higher level.
The photon energy is:
$ E=hf=\frac{hc}{\lambda} $
For hydrogen line spectra, QCE Physics can use the Rydberg equation:
$ \frac{1}{\lambda}=R\left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right) $
For emission, the initial level $n_i$ is higher than the final level $n_f$, so the bracket is positive. The Balmer series has $n_f=2$, which gives visible lines for several transitions.
Wave-particle duality
Bohr's model sits inside a broader quantum idea: matter and light can show both wave-like and particle-like behaviour. De Broglie's wavelength connects momentum to wavelength:
$ \lambda=\frac{h}{p} $
This helps explain why the standing-wave condition can be used for electrons. The electron is not just a tiny planet orbiting a nucleus; the model uses wave behaviour to explain allowed states.
The Bohr model is not the final quantum model of the atom, but in QCE Physics it is valuable because it links energy levels, line spectra and quantised angular momentum.
Worked example
Interpreting spectra
An emission spectrum has bright lines on a dark background because atoms emit specific wavelengths. An absorption spectrum has dark lines missing from a continuous spectrum because atoms absorb specific wavelengths.
Each element has its own pattern of spectral lines because each has a distinct energy-level structure. That is why line spectra can be used to identify elements in stars and gas samples.